“Invert” the neural network to find the inputangles of the forward mapping.

3 existing methods applied to IK:

Optimization: Approximate a non-linear functionbetween layers and solve using non-linearprogramming.

Iterative: Given we know the desired output lets findthe best input-output mapping to match the outputby searching a path in input space.

Error back-propagation: Plug in the desired outputinto the forward mapping network. Use back-propagation to propagate the error back to the inputunits and so the input steps along input space andlet the weights revert back to their original settingseach iteration.

Neural Network architecture

Forward kinematics can be determined for mostmanipulators except for those with redundant joints.

Good initial guess for input is made using “CornerClassification”.

Since architecture is based on equations

no

training is required!! IE, weights are taken fromequations.

Some of the weights are non-linear which makeserror back-propagation tricky. Eg, for sin and cosweights we make a decision at the neighbourhoodto determine a sign change.

Once we have convergence we test to seewhether joint angles are within their allowablerange.